Bond portfolio selction a bond portfolio manager has $100,000 to allocate to two different bonds, one corporate and one government bond. the corporate bond has a yield of 4%, a maturity of 3 years and an a rating from a rating agency that is translated into a numerical rating of 2 for computational purposes. in contrast, the government bond has a yield of 3%. a maturity of 4 years and rating of aaa with the corresponding numerical rating of 1 (lower numerical ratings correspond to higher quality bonds). the portfolio manager would like to allocate her funds so that the average rating for the portfolio is no worse than aa (numerical equivalent 1.5) and average maturity of the portfolio is at most 3.6 years. any amount not invested in the two bonds will be kept in a cash account that is assumed to earn no interest for simplicity and does ing or maturity computations (in other words, we are assuming a quality rating of 0 with ? perfect? quality and maturity of 0 vears for cash). how should the manager allocate her funds between these two bonds to achieve her not contribute to the average rat objective of maximizing the yield from this investment? » let variables x1 and x2 denote the allocation of funds to the corporate and government bond respectively (in thousands of dollars). write down the portfolio manager? s problem as a linear programming problem (not necessarily in standard form » rewrite the problem in standard form » introduce slack or surplus variables (whatever you feel is appropriate), and write down the lp problem. (you are not required to solve it).